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The War on Liquids: Disintegration and Reaction by Enhanced Pulsed Blasting
Wayne Strasser, Eastman Chemical Company, PO Box 511, Kingsport, TN, 37660, email@example.com
Under certain conditions in preferred three-stream geometries, a non-Newtonian airblast atomization flowfield violently pulses
(axially and radially) by self-generating and self-sustaining interfacial instability mechanisms. The pulsing is severe enough to send
acoustic waves throughout feed piping networks. The most recent work on this system instructed that exothermic chemical reactions
enhance this moderate Mach number atomization. Explored herein is the potential to further enhance reaction-assisted disintegration
by independently superimposing both sinusoidal and randomized mass flow fluctuations of +/- 50% of the mean onto otherwise
constant gas feed streams using surrogate models. Two nozzle geometries (low versus high prefilming distance) and multiple
superimposed feed frequencies (ranging from below to above the naturally dominant tone) are considered for each gas stream, making
twenty-one total long-running unsteady PLIC-VOF CFD models. Droplet size, plus nine other temporal measures, were considered
for assessing atomizer performance in our energy production process. Results indicate that superimposed frequencies have potential
to enhance chaotic atomization in a statistically significant manner. Depending on the geometry, the largest effect was about a 10%
reduction in droplet size; however, some combinations experienced a droplet size increase. Only marginal differences were seen in the
nine other measures, such as injector face heat exposure. In addition to the immediate industrial benefit from modulation, dramatic
changes in acoustics were produced by imposed feed perturbations at frequencies lower than the natural tone. A detailed study of
start-up flow reveals new mechanisms which explain performance differences.
KEYWORDS Acoustics; Turbulence; CFD
2-D Two dimensional
3-D Three dimensional
C Species concentration
CiCFD model case designations
CFD Computational fluid dynamics
CO Carbon monoxide
COV Coefficient of variation
D Species diffusivity
D32 Sauter mean diameter
DINozzle innermost diameter
DONozzle outermost diameter
E Total energy
g Gravity vector
H Natural system frequency
I Radiation source
IG Inner gas stream
LAG Outer annular gap
LcCharacteristic length scale
LRI Inner retraction length
M Gas/liquid momentum ratio = (U2)G/(U2)L
Ma Mach number, U/sound speed
OG Outer gas stream
Oh Ohnesorge number =
PLIC Piecewise linear interfacial construction
r Radial coordinate
Q Viscous capillary length, µ2/
R Heats of reaction source term
RAND Randomized modulation signal
RAM Random access memory
Re Reynolds number = UD/
S Velocity ratio, UG /UL
SMD Sauter mean diameter (“D32”)
SST Shear stress transport turbulence model
Sr Species reaction mass source terms
St Strouhal number, HL/U
tLI Thickness of inner lip
tLO Thickness of outer lip
tSLAN Thickness of slurry annulus
T Static temperature
u Velocity component
U Velocity magnitude
VOF Volume of fluid
We Weber number = U2LC/
Wo Womersley number =
x Axial coordinate
Z Density ratio, ρG/ρL
Phase volume fraction
γ Outer gas/liquid annular approach angle
μ Molecular viscosity
ζ Molecular thermal conductivity
Subscripts and Superscripts
i Summation index
ref Reference condition
I Inner gas
O Outer gas
INTRODUCTION AND OBJECTIVE
The disintegration of continuous liquid streams is essential to efficient operation of automotive and aircraft engines, coating
equipment, pesticide applications, phase separation devices, and energy producing industrial equipment. Atomization can be carried
out in an astounding number of ways, sometimes involving augmenting feeds of other phases. A popular configuration is air-blast (or
“air-assisted”) in which a high-momentum gas (or gases) is used to facilitate liquid breakup. As two layers of differing velocities
move past one another, an interesting array of instabilities produces liquid waves, ligaments, and eventually droplets. This is referred
to as “primary atomization” and has been studied extensively both computationally and experimentally for nearly two centuries [1-
10]. A recent investigation of instabilities, albeit with a quite simple geometry, is that of .
We now turn our attention to a three-stream, also known as “pre-filming”, design like that shown in Figure 1. A steady feed of
high-viscosity non-Newtonian slurry is sandwiched between two steady feed gas streams, which are the cylindrical inner gas (IG) and
an annular outer gas (OG). A noteworthy feature about this system is that the pulsations are not induced by any external forcing
function. Interfacial instabilities (Kelvin–Helmholtz and Rayleigh–Taylor), both inviscid mechanisms, develop as the three streams
pass near one another at high speeds. These perturbations produce waves and, eventually, liquid bridges, creating a global resonant
feedback mechanism, which in turn results in strong system pulsations and vibrations felt far upstream of the atomization region
pictured in Figure 1. Axial and radial bursting creates a highly unsteady spray field. Bulk pulsations are particularly effective in
atomization viscous material when other air-blast methodologies aren’t. For air-water test stand designs, the flow is transonic; for
slurry and high-pressure gas (realistic reactor conditions), however, the flow is subsonic with peak velocities about half the speed of
An abundance of computational and experimental studies was carried out by Strasser and colleagues on this wildly unsteady
system pursuant to exploring numerical recipes, computational setups & boundary conditions, a large set of geometric perturbations,
feed properties, feed materials, feed rates, and the incorporation of chemical reactions [12-19]. The most recent of these, 
involved a multi-objective optimization of nozzle design for heat-affected operation. Focus in [12-19] was given to validation,
developing appropriate metrics for assessing injector lifespan, establishing surrogate connections between full and reduced-order
models, and the effects of the listed issues on acoustics, atomization quality, and the thermal field. At no point in time was resolution
of all scales of turbulent motion required to meet validation.
Despite ample investigative history of this configuration and the associated discussions around the caveats and risks of using
engineering-level CFD models, there remains a remarkable prospect: What if the self-sustaining resonance could be further enhanced
with manipulations (also known as “modulation” or “excitation”)? Born in turbulence transition theory , the thought is that an
excited structure can be stimulated to a higher energy state by an external source “pumping” energy into the control volume. The
authors of  proposed that frequencies lower than the natural excitation frequency are preferred. This concept is additionally
explored in the solid-state quantum physics community [21, 22], where externally driven oscillatory systems exhibit a variety of phase
states (including stabilization) depending on how the driven energy compares with natural system dynamics. Preliminary three-stream
atomizer findings from  implied that IG stream pulsations, which play a dominant role in overall system acoustics, would move to
a more excited state when modulated. However, that work was part of a scoping effort with a 2-D (no droplet size analysis) cold-flow
model. We now endeavor to deeply probe this concept for a realistic hot-flow pulsing slurry atomizer, and the scope will be described
in the next section.
Fig. 1 Geometry for an arbitrary three-stream retracted injector
Fourteen models, shown in Table 1, involving modulation, plus a solver evaluation were considered in this work. Additionally,
six models (four of which are shaded in Table 1) were re-initialized for the purpose of start-up testing, making a total of twenty-one
new long-running unsteady simulations. Given that results of twenty-one models were sought, time did not permit (and study goals
did not warrant) the use of direct numerical simulations (DNS). Evaluated are two geometries (C1 and C4), two independently
manipulated streams (IG and OG, previously defined), and multiple sinusoidal feed driving frequencies, ranging from 250 Hz to 2000
Hz, plus a randomized driving signal. The natural system frequency (dominant tone), H, is approximately 1000 Hz, so, excluding the
randomized signal (listed as “Rand” in the table) with no defined frequency, we evaluate driving frequencies ranging from ~0.25H to
2H. In all cases, the modulated feeds are set to a magnitude of +/- 50% of the steady feed flow rates with the sine wave beginning on
the high side of the mean at time = 0.0. C1 designates a “retracted” design with a large prefilming distance (innermost nozzle
retraction LRI in Figure 1) with a value equal to 1.3 times the injector outer diameter D O, and C4 refers to a “flushed” design with
nearly zero prefilming distance. The geometric variables which remain constant are as follows: LAG, tLO , tLI, and DI are 0.10, 0.014,
0.038, and 0.36, respectively, for all simulations when scaled by the outermost diameter (DO). The angle and DO purposely remain
undisclosed, but it can be stated that DO is on the order of centimeters. Each geometry’s static feed simulation from  will be
incorporated in statistics herein as comparative baselines but are not shown in Table 1. Dimensionless groups for all tests include, Z =
0.082, Re = 180, Q = 0.053, Oh = 1.5, St = 5.4, We = 6.8x104, and Wo = 78, all on a slurry basis. For the unmodulated inner gas
stream, Wo = 3.1x103, M = 1.8, S = 4.7, Re = 5.3x106, St = 0.3, and Ma = 0.16. For the unmodulated outer gas stream, Wo = 1.7x103,
M = 12, S = 12, Re = 7.3x106, St = 0.061, and Ma = 0.41.
Table 1: Matrix of fourteen of the twenty-one studied cases
Risks related to mesh, numerics, turbulence modeling, time-step size, boundary conditions, and other modeling degrees of
freedom are undeniable. They were discussed comprehensively and exhaustively in [12-19]. Specifically, the following have already
been ensured adequate and trustworthy in those referenced works: timestep size, mesh element size relative to the slurry feature sizes,
shock waves interacting with this multiphase method, the use of an ideal gas model to treat this gas phase, the length of the modeled
domain, the azimuthal angle of the modeled domain, the ability of the code to produce and measure droplet sizes, turbulence model,
non-Newtonian (temperature- and shear-thinning) subroutine methodologies, and spatial and temporal discretization. Consequently,
the numerical setup will only be briefly highlighted here. A structured 2-D mesh was created along a plane of azimuthal symmetry.
The 2-D plane was then swept azimuthally 22.5° to produce a “wedge” 3-D model with a total of 506,000 hexahedral elements (or 8.1
million per complete 360° model). Though the geometry is azimuthally symmetric, atomization is not; therefore, periodic treatment is
given to the azimuthal bounding faces. Known property and static mass flow conditions are supplied to the inlets, and pressure-outlets
are used to handle the system outlet planes. Twelve % of the total oxidizing gas flow is administered to the inner passage. An
Eulerian-Eulerian volume of fluid (VOF) approach, which is a subset of the “mixture” two-fluid method, to this unsteady multiphase
problem is sought. Instead of assuming statistically small droplets (relative to the computational cell size) such as in , explicit
disintegrated liquid shapes (ligaments, blobs, and droplets) will be resolved. The continuity equation governing the mass balance of
each phase is:
The phase-averaged Reynolds-averaged linear momentum balance is
+ρ´u⋅∇ ´u=∇ ⋅
Gas and slurry phases share a common momentum field, so properties were arithmetically phase-averaged. Similarly, the phase-
averaged energy conservation and species conservations equations are, respectively,
Local Mach number could reach approximately 0.6 at any given time, so kinetic energy, viscous heating, and pressure-work terms are
included in Equation 3. Slurry droplet evaporation and compressibility effects were ignored. Approximating the real gray gas
absorption as a function of local composition was handled by the WSGG model .
Syngas kinetics for the cracking of water to extract energy is the industrial purpose with this atomizer. CO 2 and H2O, primarily,
are produced via the two deceptively simple highly exothermic overall reaction steps shown in equations 5 and 6. There are a
multitude of sub-steps (not shown), one which involves 6 independent equilibrium reactions. A total of 9 species were considered.
Each of the sub-step rate equations was solved simultaneously and differentially based on Arrhenius expressions, local temperature,
and the 9 local species concentrations within each computational cell.
2O2→ H 2O
The homogeneous shear stress transport (SST) two-equation linear eddy viscosity model was used for computing the turbulent
contributions to momentum, scalar, and energy transport for all cases presented herein. Equations 1 - 6 were solved in ANSYS
Fluent’s segregated double precision commercial cell-centered solver 16.2 with a Service Pack (16.2.1) for all cases except the second
row in the table, which entailed both 16.2.1 and 19.2.1 as a direct comparison. The explicit piecewise linear geometric reconstruction
scheme (PLIC) was used to reconstruct the gas-slurry interface at the sub-grid level. A typical simulation time was a few weeks on 8
Intel “i7-6700K” (4.6 GHz) cores with 3200 MHz RAM.
Preliminary Droplet Size Statistics
Prior works [12-19] addressed metrics for assessing injector lifespan, CFD validation, surrogate connections between full and
reduced-order models, and the effects of a multitude of issues on atomization quality, acoustics, and thermal field. Given that intricate
features of this near-sonic axially and radially pulsing atomized slurry field have been covered extensively, our discussion will
immediately aim towards statistical considerations of the changes induced by modulation on the acoustics, thermal landscape, and
droplet size distribution. JMP Pro version 13.1 was utilized to cull the data to remove auto-correlation. Comparisons of means and
variances were then made between the C1 unmodulated case and its modulated variants, and then between the C4 unmodulated case
and its modulated variants shown in Table 1.
Time-averaged droplet size information for the models in Table 1 plus the two base cases from  is given in Figures 2 and 3.
Figure 2 includes the slurry ligament and droplet length scale (D32, or Sauter mean diameter, SMD) versus normalized distance from
the injector tip/outlet. In all situations involving a “normalized distance” in this document, the nozzle outer diameter D O is used as the
normalization parameter. Notice that, in general, the length scales of primary disintegrated slurry are very large (on the order of mm).
This is quite large and is expected based on the effective restraining and force of slurry viscosity as is seen in the Ohnesorge number =
/Re. The SMD, in general, falls versus distance, which is what one would expect for any atomizer. Two classes of droplet
sizes result; there is a larger class produced by the retracted case, C4, and smaller droplets produced by C1. The cause of this has been
discussed at length in [12-19]. What is most interesting here, however, is that the modulated case SMD results do not massively
deviate from the steady reference cases. “C1-IG-500”, which implies geometry C1 with the inner gas external modulations being
driven at 500 Hz (or 0.5H), does show an appreciable SMD reduction but only closer to the injector tip. Similarly, some of the C4
cases show apparent SMD reductions in the middle of the sampled domain, but then they exceed the steady reference case towards the
end. The mechanism for this will be explored in the next section.
Alternatively, Figure 3 illustrates the coefficient of variation (COV, which is the temporal D32 variability within a given sampling
volume normalized by the mean) of D32 versus distance from the injector tip/outlet for the same cases as in Figure 2. This helps us
assess the droplet size distribution variability in time, or how consistent the injector is at disintegrating the slurry. Unlike the SMD
plotlines, the COV plotlines generally increase with distance from the injector. As seen with the SMD, the COV results are grouped in
two general classes. The lower COV group is that of C4, and the higher COV group is that of C1 (the opposite of the SMD grouping).
Both groups tend to converge to about 50% droplet size temporal variation towards the end of the sampled region. In other words, in
general, the slurry phase length scale temporarily varies +/- half of the mean deep in the reactor. As with the SMD, the reason for this
has been addressed in [12-19]; however, now attention is given to how the modulated cases compare to the steady reference cases.
Again, there is only moderate deviation created by modulation, with nearly all modulated C1 cases being slightly above the base case.
C1-IG-500, and especially C1-IG-250 show increased variability relative to the steady reference case closer to the injector. On the
other hand, the C4 cases show mixed results, none of which deviate much from the reference case near the injector. C4-IG-500 shows
the largest growth in atomization variability towards the domain end, while C4-IG-1000 and C4-IG-2000 become slightly more
stabilized at higher distances.
Fig. 2 Time-averaged Sauter slurry ligament and droplet length scale (D32 or SMD) versus normalized distance from the injector
tip/outlet for 14 cases in Table 1 plus the two base cases from 
Fig. 3 Coefficient of variation (COV) of D32 versus normalized distance from the injector tip/outlet for 14 cases in Table 1 plus the two
base cases from 
Statistics Involving All Measures
Comparisons of Means
The highly unsteady nature of this system creates uncertainty as to whether or not the aforementioned deviations are statistically
significant. Though mild changes have now been shown due to the effects of modulation on droplet size, care must be taken to
determine if the deviation created by modulation is more than the typical variability in time. Table 2 summarizes the findings for all
C1 cases. The columns are as follows (from left to right): the discrete normalized distance (again normalized by D O) from the injector
where the droplet size is sampled, the modulated case description, the % difference in the time-average of the measure from the
reference case, and lastly the p-Value is the probability of mistaking a difference when there is not a difference with a method
described in . The measures and cases shown therein are sorted by ascending order of modulation frequency (and then distance
from injector) and only include those cases with a p-Value of less than 0.05, or 5%. In other words, a value less than 0.05 implies that
we are 95% certain there is a difference between two means. Note that the end of the modeled domain is 2.2 nozzle outer diameters,
DO, from the tip. The inner gas modulated at 250 Hz case shows a 10% reduction in droplet size but only at one discrete measurement
location that is 1.8 outer diameters, DO, from the injector tip. There is a statistical difference, but, alone, it does not offer much
confidence that the droplet size reduction is sustained deep in the reactor. The inner gas 500 Hz case, to the contrary, shows a 10%
reduction in droplet size close to the face but a 15% increase far away from the tip; it might therefore be considered unfavorable. No
outer gas modulated cases are noteworthy.
Table 2: Statistical droplet size differences in the C1 modulated cases relative to the C1 steady reference case for only those
cases which showed a statistically significant difference
Figure 4 depicts another way of summarizing the data at the sampling location of 2 diameters from the injector tip. The mean of
all C1 cases is included with “whiskers” (95% confidence interval) on either side of the mean representing temporal variability. Only
the IG-500 simulation produces significantly different (larger) droplets than the others.
Fig. 4 Summaries of D32 means and deviations for C1 at 2 diameters from the tip
All C4 case results are presented in Table 3. Again, these are sorted in ascending order by modulation frequency and then by
distance from the tip. Relative to C1 in Table 2, more modulated cases produce measurable differences in droplet size. The only case
with sustained reductions in droplet size appears to be the one in which the inner gas is pulsed at the natural tone (“IG-1000”).
Table 3: Statistical droplet size differences in the C4 modulated cases relative to the C4 steady reference case for only those
cases which showed a statistically significant difference
Similar to Figure 4, the C4 cases at 1.5 tip diameters is displayed in Figure 5. The IG-1000 model produces notably smaller
Fig. 5 Summaries of D32 means and deviations for C4 at 1.5 diameters from the tip
The effort is now expanded beyond droplet size to include the nine other metrics discussed in  which are critical for assessing
injector reliability (e.g., injector outlet face temperature) and energy production (e.g., reactant consumption). Statistical modeling was
carried out on 9 variables among the 8 transient C1 CFD models, such that 72 comparisons were made, and a tremendous amount of
information is included herein. Twenty-eight variables were found to have a statistically significant difference between a given case
and the base case C1 model. The largest statistical difference is a 7% reduction in domain maximum temperature produced by
modulating the outer gas at 2000 Hz. The other twenty-seven measures, though statistically different, are not practically different,
where “practical” difference is defined as at least 5%.
With regard to the C4 case differences in the efficiency metrics, statistical modeling was carried out on 9 variables among the 6
transient C4 CFD models, such that 54 comparisons were made. Twenty-one variables were found to have a statistically significant
difference between a given case and the base case C4 model. The largest statistical change was that the injector face temperature
standard deviation only fell by 4% for the OG-1000 case, but this is not a practical difference. In summary, not one of the twenty-one
variables is practically different. Additionally, no remarkable differences were found by switching from solver release 16.2.1 to
Comparisons of Variances
The goal is now to investigate variables that “tune up”, or “resonate”, which implies that a given variable’s variance makes a
dramatic shift upward for a particular set of conditions. Minitab version 18.1 was used for sequential pairwise comparisons of
variances. In each case, Bonferroni confidence intervals are used to estimate the standard deviation of each population. Minitab
adjusts the Bonferroni confidence intervals to maintain the simultaneous confidence level, which decreases the chance that at least one
confidence interval does not contain the true standard deviation. Figure 6 illustrates all C1 cases’ inner gas pressure signals. The
abscissa represents the standard deviation of pressure increasing from left to right with the width of the plotted horizontal bar for each
case quantifying the 95% confidence interval about its standard deviation. The actual values of pressure standard deviation are
purposely undisclosed due to the proprietary nature of the operation, but the purpose of the figure is to illustrate that certain cases
stand out among the rest. Similar plots and comparisons were made for all cases with all variables but are not shown due to space
limitations. It can be shown that both geometries (C1 and C4) and both inner and outer gas pressures “tune up” for each of their
respective 0.5H modulated cases. In other words, the IG 500 cases show substantially increased acoustic activity in the inner gas
stream, and the OG 500 cases show the same for the outer gas stream. For C4, however, the outer gas shows tuning up for all outer
gas modulation models. Interestingly, slurry pressure fluctuations are energized for 0.25H and 0.5H inner gas modulation for C1 and
mainly only for OG-500 for C4. Aside from these mentioned, no other metric (including droplet sizes) showed meaningful
variance differences, except that the C1 IG-500 model at 0.6 normalized diameters from the nozzle showed a mildly higher
variance than the others.
Fig. 6 Comparison of variances for C1 inner gas feed pressures
Mechanism Investigation Via Startup
Though the modulated cases produced only modest changes, statistically speaking, in a total of 10 atomization performance
measures, investigations were carried out for the purpose of attempting to identify the reasons for the tuning up at 0.5H for both feed
streams and both geometries. The aim is, therefore, to explore 6 cases (C1, C1-IG-500, C1-OG-500, C4, C4-IG-500, and C4-OG-
500). In other words, we consider both geometries (C1 and C4), each with their respective inner gas and outer gas modulated cases at
0.5H. Given the vast unsteadiness of these systems, there was little hope of stopping the simulations at precisely the same time for
back-to-back visual pulsation comparisons. Instead, all 6 simulations were initiated from the same set of startup conditions: 1000 K
initial temperature, 0.5 initial oxygen mass fraction, 0.5 initial hydrogen mass fraction, and quiescent flow; note that these may or may
not be representative of plant-scale startup conditions. This way, their temporal evolution could be directly compared on a fair basis.
Every numerical setting in these simulations was the same as the quasi-steady models (Table 1), except that the timestep was reduced
by a factor of five.
To begin, an examination is made of the startup feed pressure signals of inner gas, outer gas, and slurry (respectively) in Figures
7-9. Time is normalized by the natural tone, so that the abscissa is, approximately, the number of acoustic cycles. Due to
computational resource limitations, only the first 3 cycles were simulated for the 6 startup cases. The ordinate pressure is normalized
by the peak value in the slurry feed line. Note that some cases perfectly overlap, such that they are not visible on various plots. Also
note that the differences at long time scales between the reference (unmodulated) cases have been addressed in prior work. For
example, the flushed case with no prefilming distance (C4) has less pressure drop and less pressure noise than the fully retracted case
(C1). The following conclusions about the modulated cases can be drawn from Figures 7 and 8:
1. When either gas stream is modulated, the other gas feed signal does not change from the reference case within the simulation
time; three cycles is, therefore, not enough time for the two streams to effectively communicate.
2. A given gas stream’s modulation produces pressure peaks above its baseline resonance.
3. Each stream responds nearly immediately (<0.5 cycles) to its own modulation.
Fig. 7 Normalized inner gas feed pressure signal from reactor startup for both geometry’s steady feed reference cases as well as both
gas stream modulated cases at 0.5H.
Fig. 8 Normalized outer gas feed pressure signal from reactor startup for both geometry’s steady feed reference cases as well as both
gas stream modulated cases at 0.5H.
The story told by Figure 9 is quite different. First, the slurry feed pressure responds to both gas modulations within about 2.25
cycles, instead of waiting until after 3 cycles. It makes sense that slurry responds more quickly than the feed gas signals, given that
slurry is incompressible; any acoustical changes in the prefilming region are immediately communicated to the slurry feed line.
Second, both modulated C1 cases respond the same, directionally speaking, to each gas stream’s modulation. C4 does not.
Apparently, the existence of a prefilming chamber in C1 encourages consistent responses in both streams.
Fig. 9 Normalized slurry feed pressure signal from reactor startup for both geometry’s steady feed reference cases as well as both gas
stream modulated cases at 0.5H.
Figure 10 depicts how the product conversion, normalized by the peak value from the C1 cases, responds to the startup scenario. C1
(retracted) cases appears to ramp up faster than C4 cases, in general, but both sets asymptote to the same productivity. Again, obvious
deviation from the reference cases begins before 3 cycles.
Fig. 10 Normalized product conversion response from reactor startup for both geometry’s steady feed reference cases as well as both
gas stream modulated cases at 0.5H.
An important measure for injector sustainability is the temperature on its outermost face, that which is adjacent to the reacting
chemicals. The maximum value on the face is shown versus cycle time in Figure 11. The ordinate has been normalized by the peak
value experienced during the first 3 cycles of these simulations. C1 cases peak earlier but end up being lower at 3 cycles. As with
previous figures, significant deviation from the static feed reference cases is not noticed until after 2 cycles.
Fig. 11 Normalized injector tip peak temperature response from reactor startup for both geometry’s steady feed reference cases as well
as both gas stream modulated cases at 0.5H.
Figure 12 exhibits details around the spatial COV (temperature spatial standard deviation divided by the temporal mean) for all
startup cases. With this, attention is given to the thermal stress potential in the injector face. The COV in C1 cases peaks later and
then remains higher throughout the simulations. Once again, the reaction system appears to not respond to modulation until after 2
Fig. 12 Injector tip temperature spatial COV response from reactor startup for both geometry’s steady feed reference cases as well as
both gas stream modulated cases at 0.5H.
At this point, examination will begin using dual/split contour plots on a center sampling plane. The left half of each frame
displays enstrophy from 0 to 1x108 s-2, while the right half of each frame displays turbulence kinetic energy (TKE) from 0 to 25 m2/s2.
Superimposed are grey silhouettes of the position of slurry interfaces. Case C1 at a timestamp of a half-cycle from startup is displayed
in Figure 13. The beginning of the developing slurry-gas interface is highlighted by a white arrow. At this particular sampling time,
an explosive flow (requiring the aforementioned 5x timestep size reduction) is implied by TKE and enstrophy bursting outward from
the prefilming region. This is caused by startup conditions having temperatures high enough for reactions to take place, combined
with the presence of sufficient reactant and oxidant.
Fig. 13 Instantaneous contours, with a slurry surface silhouette, at the same time (0.5 cycle from startup) for C1; the left half is colored
by enstrophy, while the right half is colored by turbulent kinetic energy.
Figure 14 offers information for the C1 flowfield at 0.5 cycle increments. The colormaps and ranges are the same as those in
Figure 13, and the 0.5 cycle time is pictured again only for the purpose of having a direct comparison with flows at later times. White
arrows mark the evolving slurry-gas interface in the lowermost frames. Up through 1.5 cycles (top row of frames), the interface has
not moved much, as the flow is still recovering from the initial ignition. Flow reversals are prevalent. Then, at 2 cycles and beyond
(bottom row), the flow is generally aligned axially, and atomization is in progress. Close examination of slurry volume fraction data
from both models suggests that slurry atomization begins at precisely 1.4 cycles for C1 and only 0.15 cycles for C4. This difference
makes sense when one considers that C4 has no prefilming distance. Another important point is that, since atomization begins before
2 cycles in both systems, atomization itself is not the cause of the aforementioned modulation differences encountered after 2 cycles.
Fig. 14 Instantaneous contours, with a slurry surface silhouette, at 0.5 cycle increments for C1; ranges and colormaps are given in
Figure 13 and are not repeated.
All 6 startup cases are now compared at a time of 3 cycles from startup in Figure 15. C1 contours (top row of frames) are
repeated for direct comparisons with the other cases. “C1I5” designates case C1 with the inner gas modulated at 500 Hz, “C1O5”
refers to C1 with the outer gas modulated at 500 Hz, and so on. Pairs of white arrows mark the features of immediate interest in the
C1 frames (top row), while only a single white arrow marks features of immediate interest in each C4 frame (bottom row). The
flowfield is more detailed than just what is marked, but space does not permit verbiage for every noteworthy item. When examining
C1 results, the uppermost marked feature is the primary toroidal vortex emanating from instabilities at the interface between the inner
gas and slurry in the prefilming region. This feature changes only slightly between the reference and the modulated cases; it is rotated
counterclockwise (in the viewing plane) slightly for I5 and O5. Upon close examination, it can also be detected that the vortex’s inner
boundary is moved radially outward by both gas mass flows surging. The white arrow at the bottom of the C1 frames indicates the
region where the enstrophy of the inside of the OG-slurry interface merges with the enstrophy of the IG-slurry interface. Inner gas
surging moves this farther down, but outer gas surging does not.
When it comes to the C4 series of models in Figure 15, the white arrow marks the secondary slurry neck; its predecessor was the
primary neck from a previous cycle shown where the slurry meets both gases. Not much changes with the secondary neck for IG
modulations, but the flowfield is radically different for OG modulation. Its secondary neck has become the tertiary neck as another
primary neck has formed.
Fig. 15 Instantaneous contours, with a slurry surface silhouette, at 3 cycles from startup for all six cases; ranges and colormaps are
given in Figure 14 and are not repeated.
Often considered is the second invariant of the deformation tensor, sometimes referred to as the “Q-criterion”, and it can be
applied as a vortex identifier . Positive values indicate that vorticity dominates over strain and that the local pressure is lower than
ambient. Negative values, on the other hand, imply that shear is the dominating factor. The Q-criterion at 3 cycles from startup on the
centerplane of all 6 startup cases is displayed in Figure 16. Although the top row (C1) and bottom row (C4) represent different
geometries, five reasonably similar flow features will be highlighted and are enumerated in the first frame of each row on the figure.
1. Outer OG-slurry interface Vortex
2. Inner OG-slurry interface Shear Layer
3. Outer IG-slurry interface Vortex
4. Merging of the inner OG-slurry interface with the outer IG-interface in the current pulse Vortex
5. Merging of the inner OG-slurry interface with the outer IG-interface from previous pulse Vortex
Modulation of streams seems to have nearly unnoticeable effects. For the C1 series, only item 3 is markedly different as was
mentioned in the discussion on Figure 15; the C1 modulated cases are nearly identical to one another. All three C4 cases, however, are
Fig. 16 Instantaneous contours of the Q-criterion, at 3 cycles from startup for all six cases.
Finally, details of startup heat generation are investigated to assess the initial formation of thermal and pressure waves. In Figure
17, contour plots of heat generation on a center plane at 0.08 cycle increments, beginning at 0.24 cycles from startup, are normalized
by a heat generation rate of >1x106 J/m3s. There are twenty frames, 5 rows of 4, and time proceeds from left to right, top to bottom.
Only the C1 steady feed reference case needs to be shown to represent all C1 cases, because the first 1.8 cycles involved in this figure
are almost identical among the three C1 models. In the first frame on the top row, two obvious regions of heat generation emerge.
The primary (more chemically active) region is at the outermost OG walls (due to a hot wall boundary condition), and the secondary
region (less chemically active) is at the moving front of the IG in the prefilming zone. Both gases are oxidants, and the ambient
contains other reactants, so heat generation around the gas interfaces is reasonable. (Note that slurry is not depicted in this figure;
from Figure 14 showing only modest slurry penetration up through 2 cycles, one may infer that slurry plays no role in ignition.)
Along the top row, the primary heat generation region changes from a torus to a contiguous region in the center, and the secondary
region grows and is slightly axially reversed at its center. The second row shows the first primary region leaving the scene and
becoming a torus again; the secondary region becomes a new primary with two sets of lobes growing, moving back onto itself, and
then shedding a layer. On the third row, the first (outer) primary region continues to wrap back onto itself along its exterior, and the
new primary region moves backward into the prefilming section along the walls. Within the fourth row, the two regions continue to
take shape such that the flow is predominantly downward. Lastly, on the fifth row, it is evident that the prefilming hot spot begins to
diffuse out. The long-term flow field was described in  and looks like a single “dancing” thin azimuthal layer of heat generation at
the exterior of the OG and no heat generation in the prefilming section.
Fig. 17 Instantaneous contours of C1 startup normalized heat generation at 0.08 cycle increments beginning at 0.24 cycles.
Figure 18 presents the same startup heat generation scenario for the C4 variants. Without the prefilming region, there is no
secondary ignition zone and no interesting flow reversals therein. Only the primary hot spot at the periphery of the OG is produced,
rolls up on itself, becomes a two-layered azimuthal feature, and the eventually tends towards it long-term character described in .
This explains the C1 versus C4 differences in Figures 9 and 10; prefilming allows a multi-tiered ignition process, such that backflow
reduces C1 slurry feed pressure (Figure 9), and C1 product conversion climbs faster (Figure 10).
Fig. 18 Instantaneous contours of C4 startup normalized heat generation at 0.08 cycle increments beginning at 0.24 cycles.
Twenty-one primary atomization engineering-level CFD simulations, in which the inner and outer gas streams of a naturally
pulsating non-Newtonian near-sonic slurry atomizer were externally and independently modulated, were run and compared with their
steady feed reference counterparts from a prior study. Surrogacy between more detailed simulations and those presented herein was
established in prior work, and at no time were DNS simulations required to validate. Sinusoidal modulation was incorporated with
frequencies ranging from a quarter to two times the natural resonant frequency; one model, however, involved a randomized external
excitation. In all cases, the flow modulation was set to +/- 50% of the respective gas phase steady feed flows. Pursuant to fully
exploring the possibly of atomization enhancement, results were given in three segments: Preliminary Droplet Size Statistics,
Rigorous Statistics Involving All Measures, and Mechanism Investigation Via Startup. Statistical considerations involved 10 measures
of atomizer performance, including droplet size, pressure drop of the three streams, and important thermal quantities. Past work
elucidated risks, validation, numerics, and boundary conditions extensively, so none of that was repeated in depth here.
Despite the fact that modulating each stream independently at half of the nozzle’s natural frequency produced interesting
amplified acoustic resonance in their respective feed streams, that amplified resonance had very little effect on droplet size and other
performance measures. Unexpectedly, it is only when modulating the streams at frequencies at or above the natural tone do significant
changes in performance metrics emerge. Forcibly pulsing the streams of the C1 (prefilming) design at, and above, its natural tone
results in modestly lower peak field temperatures. Modulating the inner gas stream of the C4 (flushed) design at its natural frequency
reduced droplet size about 10%, which is a quite important conclusion in an industry where miniscule enhancements in reactant
surface area are highly valued. Randomly pulsing the inner gas, surprisingly, seemed to have no benefit.
Startup scenarios revealed various insights. Except for the pressure of a particular modulated gas stream, modulated case metrics
do not diverge from their steady feed counterparts until about 2 flow cycles after initialization. Also, the prefilming design creates a
somewhat isolated region where secondary ignition takes place immediately after startup and facilitates increased product conversion
during initial flow development.
Overall, the ability of this system to be “tuned-up” has been demonstrated. The fact that it indeed responds measurably to
excitation is consistent with air-water atomizers showing “convective instabilities” (which implies adaptability in the response
frequency) being a preferred mode for feed momentum ratios less than ~5; our work with slurry has inner and outer gas-liquid
momentum ratios (“M”) of about 5 and 10, respectively. It is quite disappointing, however, that the dramatic acoustic changes did not
produce commensurate droplet size reductions.
The author recognizes, appreciates, and commends the excellent statistical modeling, plotting, and tabulating support of co-
worker Kevin Jones, as well as the data plotting assistance by Navya Vattikuti.
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